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<div class="title">JacobiSVD.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2009-2010 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2013-2014 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_JACOBISVD_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_JACOBISVD_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">// forward declaration (needed by ICC)</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">// the empty body is required by MSVC</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;template &lt;typename MatrixType, int Options, bool IsComplex = NumTraits&lt;typename MatrixType::Scalar&gt;::IsComplex&gt;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real {};</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">/*** QR preconditioners (R-SVD)</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment"> ***</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment"> *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment"> *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment"> *** JacobiSVD which by itself is only able to work on square matrices.</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment"> ***/</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="keyword">enum</span> { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case&gt;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">struct </span>qr_preconditioner_should_do_anything</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;{</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="keyword">enum</span> { a = MatrixType::RowsAtCompileTime != <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;             MatrixType::ColsAtCompileTime != <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;             MatrixType::ColsAtCompileTime &lt;= MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;         b = MatrixType::RowsAtCompileTime != <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;             MatrixType::ColsAtCompileTime != <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;             MatrixType::RowsAtCompileTime &lt;= MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;         ret = !( (QRPreconditioner == <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56ea2e95bc818f975b19def01e93d240dece">NoQRPreconditioner</a>) ||</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;                  (Case == PreconditionIfMoreColsThanRows &amp;&amp; <span class="keywordtype">bool</span>(a)) ||</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;                  (Case == PreconditionIfMoreRowsThanCols &amp;&amp; <span class="keywordtype">bool</span>(b)) )</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  };</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;};</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case,</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;          <span class="keywordtype">bool</span> DoAnything = qr_preconditioner_should_do_anything&lt;MatrixType, QRPreconditioner, Case&gt;::ret&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="keyword">struct </span>qr_preconditioner_impl {};</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case&gt;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, QRPreconditioner, Case, false&gt; {</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD&lt;MatrixType, Options&gt;&amp;) {}</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  <span class="keywordtype">bool</span> run(JacobiSVD&lt;MatrixType, Options&gt;&amp;, <span class="keyword">const</span> MatrixType&amp;) { <span class="keywordflow">return</span> <span class="keyword">false</span>; }</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;};</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="comment">/*** preconditioner using FullPivHouseholderQR ***/</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>, PreconditionIfMoreRowsThanCols,</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;                             true&gt; {</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  <span class="keyword">enum</span> { WorkspaceSize = MatrixType::RowsAtCompileTime, MaxWorkspaceSize = MatrixType::MaxRowsAtCompileTime };</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize&gt; WorkspaceType;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    {</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;      internal::construct_at(&amp;m_qr, svd.rows(), svd.cols());</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    }</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  }</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordflow">if</span>(matrix.rows() &gt; matrix.cols())</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    {</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;      m_qr.compute(matrix);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView&lt;Upper&gt;();</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    }</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  }</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="keyword">typedef</span> FullPivHouseholderQR&lt;MatrixType&gt; QRType;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  WorkspaceType m_workspace;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;};</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>, PreconditionIfMoreColsThanRows,</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                             true&gt; {</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160; </div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    MatrixOptions = MatrixType::Options</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  };</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::make_proper_matrix_type&lt;Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;                                                     MaxColsAtCompileTime, MaxRowsAtCompileTime&gt;::type</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;      TransposeTypeWithSameStorageOrder;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;      internal::construct_at(&amp;m_qr, svd.cols(), svd.rows());</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  }</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <span class="keywordflow">if</span>(matrix.cols() &gt; matrix.rows())</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    {</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView&lt;Upper&gt;().adjoint();</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  <span class="keyword">typedef</span> FullPivHouseholderQR&lt;TransposeTypeWithSameStorageOrder&gt; QRType;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="keyword">typename</span> plain_row_type&lt;MatrixType&gt;::type m_workspace;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;};</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">/*** preconditioner using ColPivHouseholderQR ***/</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160; </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd2e2f4875c5b4b6e602a433d90c4e5e">ColPivHouseholderQRPreconditioner</a>, PreconditionIfMoreRowsThanCols,</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;                             true&gt; {</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    WorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixUColsAtCompileTime,</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    MaxWorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixUMaxColsAtCompileTime</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  };</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize&gt; WorkspaceType;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;      internal::construct_at(&amp;m_qr, svd.rows(), svd.cols());</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (svd.m_computeThinU) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordflow">if</span>(matrix.rows() &gt; matrix.cols())</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    {</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      m_qr.compute(matrix);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView&lt;Upper&gt;();</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinU)</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      {</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      }</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;      <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    }</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  }</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160; </div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  <span class="keyword">typedef</span> ColPivHouseholderQR&lt;MatrixType&gt; QRType;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  WorkspaceType m_workspace;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;};</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd2e2f4875c5b4b6e602a433d90c4e5e">ColPivHouseholderQRPreconditioner</a>, PreconditionIfMoreColsThanRows,</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                             true&gt; {</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160; </div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    MatrixOptions = MatrixType::Options,</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    WorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixVColsAtCompileTime,</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    MaxWorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixVMaxColsAtCompileTime</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  };</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1&gt; WorkspaceType;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::make_proper_matrix_type&lt;Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                                                     MaxColsAtCompileTime, MaxRowsAtCompileTime&gt;::type</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      TransposeTypeWithSameStorageOrder;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160; </div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    {</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;      internal::construct_at(&amp;m_qr, svd.cols(), svd.rows());</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    }</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (svd.m_computeThinV) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  }</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    <span class="keywordflow">if</span>(matrix.cols() &gt; matrix.rows())</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    {</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;      m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;      m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160; </div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView&lt;Upper&gt;().adjoint();</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinV)</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;      {</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;      }</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;      <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    }</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  }</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160; </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  <span class="keyword">typedef</span> ColPivHouseholderQR&lt;TransposeTypeWithSameStorageOrder&gt; QRType;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  WorkspaceType m_workspace;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;};</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="comment">/*** preconditioner using HouseholderQR ***/</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56ea9c660eb3336bf8c77ce9d081ca07cbdd">HouseholderQRPreconditioner</a>, PreconditionIfMoreRowsThanCols, true&gt; {</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    WorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixUColsAtCompileTime,</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    MaxWorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixUMaxColsAtCompileTime</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  };</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize&gt; WorkspaceType;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    {</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;      internal::construct_at(&amp;m_qr, svd.rows(), svd.cols());</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    }</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (svd.m_computeThinU) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  }</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    <span class="keywordflow">if</span>(matrix.rows() &gt; matrix.cols())</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;    {</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;      m_qr.compute(matrix);</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView&lt;Upper&gt;();</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinU)</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;      {</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;      }</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;      <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    }</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  }</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="keyword">typedef</span> HouseholderQR&lt;MatrixType&gt; QRType;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  WorkspaceType m_workspace;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;};</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160; </div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;<span class="keyword">class </span>qr_preconditioner_impl&lt;MatrixType, Options, <a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56ea9c660eb3336bf8c77ce9d081ca07cbdd">HouseholderQRPreconditioner</a>, PreconditionIfMoreColsThanRows, true&gt; {</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVDType;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160; </div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    MatrixOptions = MatrixType::Options,</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    WorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixVColsAtCompileTime,</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    MaxWorkspaceSize = internal::traits&lt;SVDType&gt;::MatrixVMaxColsAtCompileTime</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  };</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160; </div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1&gt; WorkspaceType;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160; </div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::make_proper_matrix_type&lt;Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;                                                     MaxColsAtCompileTime, MaxRowsAtCompileTime&gt;::type</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;      TransposeTypeWithSameStorageOrder;</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160; </div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> SVDType&amp; svd) {</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    {</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;      internal::destroy_at(&amp;m_qr);</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;      internal::construct_at(&amp;m_qr, svd.cols(), svd.rows());</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;    }</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordflow">if</span> (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (svd.m_computeThinV) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  }</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160; </div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keywordtype">bool</span> run(SVDType&amp; svd, <span class="keyword">const</span> MatrixType&amp; matrix) {</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <span class="keywordflow">if</span>(matrix.cols() &gt; matrix.rows())</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    {</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;      m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;      m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160; </div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView&lt;Upper&gt;().adjoint();</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinV)</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      {</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;      }</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;    }</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  }</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160; </div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  <span class="keyword">typedef</span> HouseholderQR&lt;TransposeTypeWithSameStorageOrder&gt; QRType;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;  QRType m_qr;</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  WorkspaceType m_workspace;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;};</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160; </div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;<span class="comment">/*** 2x2 SVD implementation</span></div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;<span class="comment"> ***</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="comment"> *** JacobiSVD consists in performing a series of 2x2 SVD subproblems</span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;<span class="comment"> ***/</span></div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real&lt;MatrixType, Options, false&gt; {</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVD;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">bool</span> run(<span class="keyword">typename</span> SVD::WorkMatrixType&amp;, SVD&amp;, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>, RealScalar&amp;) { <span class="keywordflow">return</span> <span class="keyword">true</span>; }</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;};</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160; </div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real&lt;MatrixType, Options, true&gt; {</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <span class="keyword">typedef</span> JacobiSVD&lt;MatrixType, Options&gt; SVD;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">bool</span> run(<span class="keyword">typename</span> SVD::WorkMatrixType&amp; work_matrix, SVD&amp; svd, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> q, RealScalar&amp; maxDiagEntry)</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  {</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    Scalar z;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    JacobiRotation&lt;Scalar&gt; rot;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    RealScalar n = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160; </div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    <span class="keyword">const</span> RealScalar considerAsZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="keyword">const</span> RealScalar precision = NumTraits&lt;Scalar&gt;::epsilon();</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160; </div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    <span class="keywordflow">if</span>(numext::is_exactly_zero(n))</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    {</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;      <span class="comment">// make sure first column is zero</span></div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;      work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160; </div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(numext::imag(work_matrix.coeff(p,q)))&gt;considerAsZero)</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;      {</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;        <span class="comment">// work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;        z = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;        work_matrix.row(p) *= z;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;        <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(p) *= <a class="code" href="namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">conj</a>(z);</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      }</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(numext::imag(work_matrix.coeff(q,q)))&gt;considerAsZero)</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      {</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;        z = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;        work_matrix.row(q) *= z;</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(q) *= <a class="code" href="namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">conj</a>(z);</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;      }</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;      <span class="comment">// otherwise the second row is already zero, so we have nothing to do.</span></div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    }</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    {</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;      rot.c() = <a class="code" href="namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">conj</a>(work_matrix.coeff(p,p)) / n;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;      rot.s() = work_matrix.coeff(q,p) / n;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;      work_matrix.applyOnTheLeft(p,q,rot);</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;      <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(numext::imag(work_matrix.coeff(p,q)))&gt;considerAsZero)</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;      {</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        z = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        work_matrix.col(q) *= z;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;        <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV.col(q) *= z;</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;      }</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(numext::imag(work_matrix.coeff(q,q)))&gt;considerAsZero)</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;      {</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;        z = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;        work_matrix.row(q) *= z;</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;        <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(q) *= <a class="code" href="namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">conj</a>(z);</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;      }</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    }</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160; </div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    <span class="comment">// update largest diagonal entry</span></div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    maxDiagEntry = numext::maxi&lt;RealScalar&gt;(maxDiagEntry,numext::maxi&lt;RealScalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(p,p)), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(q,q))));</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    <span class="comment">// and check whether the 2x2 block is already diagonal</span></div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    RealScalar threshold = numext::maxi&lt;RealScalar&gt;(considerAsZero, precision * maxDiagEntry);</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(p,q))&gt;threshold || <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(work_matrix.coeff(q,p)) &gt; threshold;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  }</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;};</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160; </div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;<span class="keyword">struct </span>traits&lt;JacobiSVD&lt;MatrixType_, Options&gt; &gt; : svd_traits&lt;MatrixType_, Options&gt; {</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;};</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160; </div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160; </div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options_&gt;</div>
<div class="line"><a name="l00514"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html">  514</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>&lt;JacobiSVD&lt;MatrixType_, Options_&gt; &gt; {</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase&lt;JacobiSVD&gt;</a> <a class="code" href="structEigen_1_1EigenBase.html">Base</a>;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160; </div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::Scalar Scalar;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::RealScalar RealScalar;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Base::Index</a> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>;</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;    Options = Options_,</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;    QRPreconditioner = internal::get_qr_preconditioner(Options),</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;    RowsAtCompileTime = Base::RowsAtCompileTime,</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    ColsAtCompileTime = Base::ColsAtCompileTime,</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;    DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    MaxColsAtCompileTime = Base::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;    MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    MatrixOptions = Base::MatrixOptions</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;  };</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160; </div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::MatrixUType MatrixUType;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::MatrixVType MatrixVType;</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::SingularValuesType SingularValuesType;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix</a>&lt;Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime,</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;                 MaxDiagSizeAtCompileTime&gt;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;      <a class="code" href="classEigen_1_1Matrix.html">WorkMatrixType</a>;</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160; </div>
<div class="line"><a name="l00546"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a3a7278d7c7eaad2e2d72f97ff95348a5">  546</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html#a3a7278d7c7eaad2e2d72f97ff95348a5">JacobiSVD</a>() {}</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160; </div>
<div class="line"><a name="l00555"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a88ca74e82c78d8ee9df7dc040e8a7b66">  555</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html#a88ca74e82c78d8ee9df7dc040e8a7b66">JacobiSVD</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>) { allocate(<a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, internal::get_computation_options(Options)); }</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160; </div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  EIGEN_DEPRECATED</div>
<div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a3a8f6a214ed1eee6af68bba23c1b2d38">  572</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html#a3a8f6a214ed1eee6af68bba23c1b2d38">JacobiSVD</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(computationOptions, <a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;    allocate(<a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, computationOptions);</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  }</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160; </div>
<div class="line"><a name="l00582"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#aa6e3accc575a9fd7166dc5f25eb12bf0">  582</a></span>&#160;  <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1JacobiSVD.html#aa6e3accc575a9fd7166dc5f25eb12bf0">JacobiSVD</a>(<span class="keyword">const</span> MatrixType&amp; matrix) { compute_impl(matrix, internal::get_computation_options(Options)); }</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160; </div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;  <span class="comment">// EIGEN_DEPRECATED // TODO(cantonios): re-enable after fixing a few 3p libraries that error on deprecation warnings.</span></div>
<div class="line"><a name="l00597"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a6fe7723c6325f58a2e228f51698f8b50">  597</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html#a6fe7723c6325f58a2e228f51698f8b50">JacobiSVD</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;    compute_impl(matrix, computationOptions);</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;  }</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160; </div>
<div class="line"><a name="l00607"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a9f481abc476101dd1ae0491de39973aa">  607</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a>&amp; <a class="code" href="classEigen_1_1JacobiSVD.html#a9f481abc476101dd1ae0491de39973aa">compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix) { <span class="keywordflow">return</span> compute_impl(matrix, m_computationOptions); }</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160; </div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  EIGEN_DEPRECATED</div>
<div class="line"><a name="l00619"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a0139ce8bcb22ba1ec10e48c28ed0b1b1">  619</a></span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a>&amp; <a class="code" href="classEigen_1_1JacobiSVD.html#a0139ce8bcb22ba1ec10e48c28ed0b1b1">compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(m_computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;    <span class="keywordflow">return</span> compute_impl(matrix, computationOptions);</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  }</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  <span class="keyword">using</span> <a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">Base::computeU</a>;</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;  <span class="keyword">using</span> <a class="code" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">Base::computeV</a>;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="keyword">using</span> Base::rows;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  <span class="keyword">using</span> Base::cols;</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  <span class="keyword">using</span> <a class="code" href="classEigen_1_1SVDBase.html#a30b89e24f42f1692079eea31b361d26a">Base::rank</a>;</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160; </div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;  <span class="keywordtype">void</span> allocate(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a>&amp; compute_impl(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160; </div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160; <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;  <span class="keyword">using</span> Base::m_cols;</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;  <span class="keyword">using</span> Base::m_computationOptions;</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;  <span class="keyword">using</span> Base::m_computeFullU;</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;  <span class="keyword">using</span> Base::m_computeFullV;</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;  <span class="keyword">using</span> Base::m_computeThinU;</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;  <span class="keyword">using</span> Base::m_computeThinV;</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;  <span class="keyword">using</span> Base::m_diagSize;</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;  <span class="keyword">using</span> Base::m_isAllocated;</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;  <span class="keyword">using</span> Base::m_matrixU;</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;  <span class="keyword">using</span> Base::m_matrixV;</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;  <span class="keyword">using</span> Base::m_nonzeroSingularValues;</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  <span class="keyword">using</span> Base::m_prescribedThreshold;</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;  <span class="keyword">using</span> Base::m_rows;</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  <span class="keyword">using</span> Base::m_singularValues;</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <span class="keyword">using</span> Base::m_usePrescribedThreshold;</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;  <span class="keyword">using</span> Base::ShouldComputeThinU;</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;  <span class="keyword">using</span> Base::ShouldComputeThinV;</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160; </div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;  EIGEN_STATIC_ASSERT(!(ShouldComputeThinU &amp;&amp; <span class="keywordtype">int</span>(QRPreconditioner) == <span class="keywordtype">int</span>(<a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>)) &amp;&amp;</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;                          !(ShouldComputeThinU &amp;&amp; <span class="keywordtype">int</span>(QRPreconditioner) == <span class="keywordtype">int</span>(<a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>)),</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;                      <span class="stringliteral">&quot;JacobiSVD: can&#39;t compute thin U or thin V with the FullPivHouseholderQR preconditioner. &quot;</span></div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;                      <span class="stringliteral">&quot;Use the ColPivHouseholderQR preconditioner instead.&quot;</span>)</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160; </div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;  template &lt;typename MatrixType__, <span class="keywordtype">int</span> Options__, <span class="keywordtype">bool</span> IsComplex_&gt;</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  friend struct internal::svd_precondition_2x2_block_to_be_real;</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;  template &lt;typename MatrixType__, <span class="keywordtype">int</span> Options__, <span class="keywordtype">int</span> QRPreconditioner_, <span class="keywordtype">int</span> Case_, <span class="keywordtype">bool</span> DoAnything_&gt;</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;  friend struct internal::qr_preconditioner_impl;</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160; </div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;  internal::qr_preconditioner_impl&lt;MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreColsThanRows&gt;</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;      m_qr_precond_morecols;</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;  internal::qr_preconditioner_impl&lt;MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols&gt;</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;      m_qr_precond_morerows;</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  WorkMatrixType m_workMatrix;</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;  MatrixType m_scaledMatrix;</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;};</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;template &lt;typename MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a>&lt;MatrixType, Options&gt;::allocate(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;  <span class="keywordflow">if</span> (Base::allocate(<a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, computationOptions)) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160; </div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;  eigen_assert(!(ShouldComputeThinU &amp;&amp; <span class="keywordtype">int</span>(QRPreconditioner) == <span class="keywordtype">int</span>(<a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>)) &amp;&amp;</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;               !(ShouldComputeThinU &amp;&amp; <span class="keywordtype">int</span>(QRPreconditioner) == <span class="keywordtype">int</span>(<a class="code" href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">FullPivHouseholderQRPreconditioner</a>)) &amp;&amp;</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;               <span class="stringliteral">&quot;JacobiSVD: can&#39;t compute thin U or thin V with the FullPivHouseholderQR preconditioner. &quot;</span></div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;               <span class="stringliteral">&quot;Use the ColPivHouseholderQR preconditioner instead.&quot;</span>);</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160; </div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;  m_workMatrix.resize(m_diagSize, m_diagSize);</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;  <span class="keywordflow">if</span>(m_cols&gt;m_rows)   m_qr_precond_morecols.allocate(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keywordflow">if</span>(m_rows&gt;m_cols)   m_qr_precond_morerows.allocate(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  <span class="keywordflow">if</span>(m_rows!=m_cols)  m_scaledMatrix.resize(<a class="code" href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>,<a class="code" href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>);</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;}</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160; </div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;JacobiSVD&lt;MatrixType, Options&gt;&amp; JacobiSVD&lt;MatrixType, Options&gt;::compute_impl(<span class="keyword">const</span> MatrixType&amp; matrix,</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;                                                                             <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160; </div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;  allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160; </div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;  <span class="comment">// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,</span></div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  <span class="comment">// only worsening the precision of U and V as we accumulate more rotations</span></div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  <span class="keyword">const</span> RealScalar precision = RealScalar(2) * NumTraits&lt;Scalar&gt;::epsilon();</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160; </div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;  <span class="comment">// limit for denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)</span></div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;  <span class="keyword">const</span> RealScalar considerAsZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160; </div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="comment">// Scaling factor to reduce over/under-flows</span></div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;  RealScalar scale = matrix.cwiseAbs().template maxCoeff&lt;PropagateNaN&gt;();</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  <span class="keywordflow">if</span> (!(numext::isfinite)(scale)) {</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;    m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">InvalidInput</a>;</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;  }</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;  <span class="keywordflow">if</span>(numext::is_exactly_zero(scale)) scale = RealScalar(1);</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  </div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;<span class="comment">  /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */</span></div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160; </div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;  <span class="keywordflow">if</span>(m_rows!=m_cols)</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;  {</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;    m_scaledMatrix = matrix / scale;</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;    m_qr_precond_morecols.run(*<span class="keyword">this</span>, m_scaledMatrix);</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;    m_qr_precond_morerows.run(*<span class="keyword">this</span>, m_scaledMatrix);</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;  }</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;  {</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;    m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;    <span class="keywordflow">if</span>(m_computeFullU) m_matrixU.<a class="code" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">setIdentity</a>(m_rows,m_rows);</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;    <span class="keywordflow">if</span>(m_computeThinU) m_matrixU.<a class="code" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">setIdentity</a>(m_rows,m_diagSize);</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;    <span class="keywordflow">if</span>(m_computeFullV) m_matrixV.<a class="code" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">setIdentity</a>(m_cols,m_cols);</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;    <span class="keywordflow">if</span>(m_computeThinV) m_matrixV.<a class="code" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">setIdentity</a>(m_cols, m_diagSize);</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;  }</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160; </div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;<span class="comment">  /*** step 2. The main Jacobi SVD iteration. ***/</span></div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;  RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160; </div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;  <span class="keywordtype">bool</span> finished = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;  <span class="keywordflow">while</span>(!finished)</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;  {</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;    finished = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160; </div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;    <span class="comment">// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix</span></div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160; </div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;    <span class="keywordflow">for</span>(Index p = 1; p &lt; m_diagSize; ++p)</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;    {</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;      <span class="keywordflow">for</span>(Index q = 0; q &lt; p; ++q)</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;      {</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;        <span class="comment">// if this 2x2 sub-matrix is not diagonal already...</span></div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;        <span class="comment">// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN&#39;s don&#39;t</span></div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;        <span class="comment">// keep us iterating forever. Similarly, small denormal numbers are considered zero.</span></div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;        RealScalar <a class="code" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold</a> = numext::maxi&lt;RealScalar&gt;(considerAsZero, precision * maxDiagEntry);</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;        <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_workMatrix.coeff(p,q))&gt;<a class="code" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold</a> || <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_workMatrix.coeff(q,p)) &gt; <a class="code" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold</a>)</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;        {</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;          finished = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;          <span class="comment">// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal</span></div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;          <span class="comment">// the complex to real operation returns true if the updated 2x2 block is not already diagonal</span></div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;          <span class="keywordflow">if</span> (internal::svd_precondition_2x2_block_to_be_real&lt;MatrixType, Options&gt;::run(m_workMatrix, *<span class="keyword">this</span>, p, q,</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;                                                                                        maxDiagEntry)) {</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;            JacobiRotation&lt;RealScalar&gt; j_left, j_right;</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;            internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &amp;j_left, &amp;j_right);</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160; </div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;            <span class="comment">// accumulate resulting Jacobi rotations</span></div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;            m_workMatrix.applyOnTheLeft(p,q,j_left);</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;            <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">computeU</a>()) m_matrixU.<a class="code" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">applyOnTheRight</a>(p,q,j_left.transpose());</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160; </div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;            m_workMatrix.applyOnTheRight(p,q,j_right);</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;            <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">computeV</a>()) m_matrixV.<a class="code" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">applyOnTheRight</a>(p,q,j_right);</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160; </div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;            <span class="comment">// keep track of the largest diagonal coefficient</span></div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;            maxDiagEntry = numext::maxi&lt;RealScalar&gt;(maxDiagEntry,numext::maxi&lt;RealScalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_workMatrix.coeff(p,p)), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_workMatrix.coeff(q,q))));</div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;          }</div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;        }</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;      }</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;    }</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;  }</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160; </div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;<span class="comment">  /*** step 3. The work matrix is now diagonal, so ensure it&#39;s positive so its diagonal entries are the singular values ***/</span></div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160; </div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;  <span class="keywordflow">for</span>(Index i = 0; i &lt; m_diagSize; ++i)</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;  {</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;    <span class="comment">// For a complex matrix, some diagonal coefficients might note have been</span></div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;    <span class="comment">// treated by svd_precondition_2x2_block_to_be_real, and the imaginary part</span></div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;    <span class="comment">// of some diagonal entry might not be null.</span></div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;    <span class="keywordflow">if</span>(NumTraits&lt;Scalar&gt;::IsComplex &amp;&amp; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(numext::imag(m_workMatrix.coeff(i,i)))&gt;considerAsZero)</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;    {</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;      RealScalar a = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_workMatrix.coeff(i,i));</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;      m_singularValues.coeffRef(i) = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(a);</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">computeU</a>()) m_matrixU.col(i) *= m_workMatrix.<a class="code" href="classEigen_1_1PlainObjectBase.html#a954cd075bcd7babb429e3e4b9a418651">coeff</a>(i,i)/a;</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;    }</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;    {</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;      <span class="comment">// m_workMatrix.coeff(i,i) is already real, no difficulty:</span></div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;      RealScalar a = numext::real(m_workMatrix.coeff(i,i));</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;      m_singularValues.coeffRef(i) = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(a);</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">computeU</a>() &amp;&amp; (a&lt;RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;    }</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;  }</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;  </div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;  m_singularValues *= scale;</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160; </div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;<span class="comment">  /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/</span></div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160; </div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;  m_nonzeroSingularValues = m_diagSize;</div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;  <span class="keywordflow">for</span>(Index i = 0; i &lt; m_diagSize; i++)</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;  {</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> pos;</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;    RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSize-i).maxCoeff(&amp;pos);</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;    <span class="keywordflow">if</span>(numext::is_exactly_zero(maxRemainingSingularValue))</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;    {</div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;      m_nonzeroSingularValues = i;</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;    }</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;    <span class="keywordflow">if</span>(pos)</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;    {</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;      pos += i;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;      std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">computeU</a>()) m_matrixU.col(pos).<a class="code" href="classEigen_1_1DenseBase.html#af9e7e4305fdb7781f2b2f05fa801f21e">swap</a>(m_matrixU.col(i));</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;      <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">computeV</a>()) m_matrixV.col(pos).<a class="code" href="classEigen_1_1DenseBase.html#af9e7e4305fdb7781f2b2f05fa801f21e">swap</a>(m_matrixV.col(i));</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;    }</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;  }</div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160; </div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;}</div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160; </div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00829"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a60d9abc5326bd9da36e437141af2daec">  829</a></span>&#160;<a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>, Options&gt; <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;::jacobiSvd</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD&lt;PlainObject, Options&gt;</a>(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;}</div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160; </div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;<a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>, Options&gt; <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;::jacobiSvd</a>(</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD&lt;PlainObject, Options&gt;</a>(*<span class="keyword">this</span>, computationOptions);</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;}</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160; </div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160; </div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_JACOBISVD_H</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_af9e7e4305fdb7781f2b2f05fa801f21e"><div class="ttname"><a href="classEigen_1_1DenseBase.html#af9e7e4305fdb7781f2b2f05fa801f21e">Eigen::DenseBase::swap</a></div><div class="ttdeci">void swap(const DenseBase&lt; OtherDerived &gt; &amp;other)</div><div class="ttdef"><b>Definition:</b> DenseBase.h:409</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html">Eigen::JacobiSVD</a></div><div class="ttdoc">Two-sided Jacobi SVD decomposition of a rectangular matrix.</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:514</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a0139ce8bcb22ba1ec10e48c28ed0b1b1"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a0139ce8bcb22ba1ec10e48c28ed0b1b1">Eigen::JacobiSVD::compute</a></div><div class="ttdeci">EIGEN_DEPRECATED JacobiSVD &amp; compute(const MatrixType &amp;matrix, unsigned int computationOptions)</div><div class="ttdoc">Method performing the decomposition of given matrix, as specified by the computationOptions parameter...</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:619</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::JacobiSVD::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a3a7278d7c7eaad2e2d72f97ff95348a5"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a3a7278d7c7eaad2e2d72f97ff95348a5">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:546</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a3a8f6a214ed1eee6af68bba23c1b2d38"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a3a8f6a214ed1eee6af68bba23c1b2d38">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">EIGEN_DEPRECATED JacobiSVD(Index rows, Index cols, unsigned int computationOptions)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:572</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a6fe7723c6325f58a2e228f51698f8b50"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a6fe7723c6325f58a2e228f51698f8b50">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD(const MatrixType &amp;matrix, unsigned int computationOptions)</div><div class="ttdoc">Constructor performing the decomposition of given matrix using specified options for computing unitar...</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:597</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a88ca74e82c78d8ee9df7dc040e8a7b66"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a88ca74e82c78d8ee9df7dc040e8a7b66">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:555</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_a9f481abc476101dd1ae0491de39973aa"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a9f481abc476101dd1ae0491de39973aa">Eigen::JacobiSVD::compute</a></div><div class="ttdeci">JacobiSVD &amp; compute(const MatrixType &amp;matrix)</div><div class="ttdoc">Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified us...</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:607</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_aa6e3accc575a9fd7166dc5f25eb12bf0"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#aa6e3accc575a9fd7166dc5f25eb12bf0">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD(const MatrixType &amp;matrix)</div><div class="ttdoc">Constructor performing the decomposition of given matrix, using the custom options specified with the...</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:582</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::JacobiSVD::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a18e969adfdf2db4ac44c47fbdc854683"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">Eigen::MatrixBase::setIdentity</a></div><div class="ttdeci">Derived &amp; setIdentity()</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:875</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a45d91752925d2757fc8058a293b15462"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">Eigen::MatrixBase::applyOnTheRight</a></div><div class="ttdeci">void applyOnTheRight(const EigenBase&lt; OtherDerived &gt; &amp;other)</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:533</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a954cd075bcd7babb429e3e4b9a418651"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a954cd075bcd7babb429e3e4b9a418651">Eigen::PlainObjectBase::coeff</a></div><div class="ttdeci">const Scalar &amp; coeff(Index rowId, Index colId) const</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:164</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html"><div class="ttname"><a href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a></div><div class="ttdoc">Base class of SVD algorithms.</div><div class="ttdef"><b>Definition:</b> SVDBase.h:120</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a30b89e24f42f1692079eea31b361d26a"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a30b89e24f42f1692079eea31b361d26a">Eigen::SVDBase::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:222</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a5f12efcb791eb007d4a4890ac5255ac4"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">Eigen::SVDBase::computeV</a></div><div class="ttdeci">bool computeV() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:284</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a705a7c2709e1624ccc19aa748a78d473"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">Eigen::SVDBase::computeU</a></div><div class="ttdeci">bool computeU() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:282</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a98b2ee98690358951807353812a05c69"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">Eigen::SVDBase&lt; JacobiSVD&lt; MatrixType_, Options_ &gt; &gt;::threshold</a></div><div class="ttdeci">RealScalar threshold() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:272</div></div>
<div class="ttc" id="agroup__enums_html_gga46eba0d5c621f590b8cf1b53af31d56ea2e95bc818f975b19def01e93d240dece"><div class="ttname"><a href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56ea2e95bc818f975b19def01e93d240dece">Eigen::NoQRPreconditioner</a></div><div class="ttdeci">@ NoQRPreconditioner</div><div class="ttdef"><b>Definition:</b> Constants.h:429</div></div>
<div class="ttc" id="agroup__enums_html_gga46eba0d5c621f590b8cf1b53af31d56ea9c660eb3336bf8c77ce9d081ca07cbdd"><div class="ttname"><a href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56ea9c660eb3336bf8c77ce9d081ca07cbdd">Eigen::HouseholderQRPreconditioner</a></div><div class="ttdeci">@ HouseholderQRPreconditioner</div><div class="ttdef"><b>Definition:</b> Constants.h:431</div></div>
<div class="ttc" id="agroup__enums_html_gga46eba0d5c621f590b8cf1b53af31d56eabd2e2f4875c5b4b6e602a433d90c4e5e"><div class="ttname"><a href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd2e2f4875c5b4b6e602a433d90c4e5e">Eigen::ColPivHouseholderQRPreconditioner</a></div><div class="ttdeci">@ ColPivHouseholderQRPreconditioner</div><div class="ttdef"><b>Definition:</b> Constants.h:427</div></div>
<div class="ttc" id="agroup__enums_html_gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50"><div class="ttname"><a href="group__enums.html#gga46eba0d5c621f590b8cf1b53af31d56eabd745dcaff7019c5f918c68809e5ea50">Eigen::FullPivHouseholderQRPreconditioner</a></div><div class="ttdeci">@ FullPivHouseholderQRPreconditioner</div><div class="ttdef"><b>Definition:</b> Constants.h:433</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">Eigen::InvalidInput</a></div><div class="ttdeci">@ InvalidInput</div><div class="ttdef"><b>Definition:</b> Constants.h:451</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ab84f39a06a18e1ebb23f8be80345b79d"><div class="ttname"><a href="namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">Eigen::conj</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_conjugate_op&lt; typename Derived::Scalar &gt;, const Derived &gt; conj(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
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